Tool path measurement

ABSTRACT

The degree of accuracy a machine tool or the like is moved along a given path is determined by a unique preferably laser beam directing measuring system directing simultaneously or in sequence a laser beam parallel to the orthogonal axes of the two or three dimensional space in which the spindle or other object is to be moved in a path which can diverge appreciably in directions other than the directions of these axes. The beam directing means includes means which provides a measure of the actual positions the object has at various sampling times relative to the axis along which the beam is directed. This actual path position data is compared to the desired path position data used to program the object moving machine to determine the path position error at the sampling times involved.

I. RELATED APPLICATIONS

This application is based on U.S. Provisional Application Ser. No.60/112,101, filed Dec. 14, 1998. This application is acontinuation-in-part of PCT Application Serial. No. PCT/US 99/14815filed Jun. 29, 1999 and its corresponding Provisional applications inthat the latter application(s) disclose(s) in FIGS. 10a, 10 b and 10 cthereof unique laser interferometer object displacement measuringsystems useable also in the present invention and recited in some of theclaims and disclosed respectively in FIGS. 1, 3A and 3 herein.

II. BACKGROUND OF INVENTION

For the machining of precision and quality parts, it is important tomeasure the machine accuracy and performance both at static conditions(low speed or stopped) and at dynamic conditions (high speed andmultiple-axis). Laser interferometers have been used for the measurementof machine positioning accuracy at static conditions and relative to theposition accuracy along each of the axes involved. That is, themeasurements were not taken as the machine spindle was moving relativeto the X, Y and Z axes involved for reasons including the fact that thelaser systems which reflected a laser beam off of a retroreflectorcarried by the spindle could not intercept the reflected beam to make ameasurement as the spindle was intentionally moved appreciably relativeto these axes. The laser interferometer systems disclosed in said PCTapplication Ser. No. US 99/14815 do not have this severe problem.

A prior art device which can make such measurements but under relativelylow speed circular spindle movement conditions uses a telescopingball-bar (sometimes called double ball-bar or ball-bar).

The ball-bar consists of two steel balls supported by two three-pointcontact magnetic sockets, which are clamped to the spindle nose and onthe table of the machine. The balls are connected by a telescoping bar,and movement is detected by a transducer similar to a linear variabledifferential transformer. The ball clamped on the table socket is thecenter of rotation, while the ball on the spindle socket performscircular motions.

The control system moves the spindle around a circle having the sameradius as the ballbar's length. As the path deviates from a perfectcircle, the change in distance between the two ends of the device ismeasured by the transducer. Hence, the deviations in circularinterpolation or machine geometry are detected by the telescopingballbar. The data collected is then plotted in a polar coordinate andcompared with a perfect circle.

Telescoping ballbar systems normally work with radii of 50 to 600 mm.

The invention described herein uses laser measurement systems like thatdisclosed in said PCT application in a manner which can measure spindledisplacement error under conditions where the spindle is stopped orpreferably is moved at high speeds in circular or other pathconfigurations. In contrast to the ball-bar technique, the presentinvention is able presently to measure spindle displacements accuratelyfor circular path radii varied continuously from as small as 1 mm(1/50th of the minimum ball-bar size) to 150 mm and larger at feed ratesup to 4 m/sec. at a data rate up to 1000 data points per second with afile size up to 10,000 data points per run.

A 2-dimensional grid encoder model KGM 101, manufactured by Heidenhain,Traunrent, Germany, can be used to determine the tool path and sharpcornering. (A 2-dimensional grid encoder is similar to a glass scalelinear encoder, except that the grid pattern used is 2-dimensionalinstead of 1-dimensional so that it is able to measure the displacementin two directions, that is in a plane.) However, this 2-dimensionalsystem is very expensive and difficult to use. Furthermore, the gapbetween the reader head and the grid plate used therein is very small,so careful alignment is necessary to avoid a crash and damage to theglass scale.

There are many inferior prior art laser interferometer techniques fortool path measurement. For example, K. C. Lau and R. J. Hocken hasdeveloped three and five axis laser tracking systems (see U.S. Pat. No.4,714,339, granted Dec. 22, 1987.) This patent discloses a laserinterferometer using a retroreflector as target, another laser beamreflecting device and a quad-detector tracking device to point the laserbeam always at the retroreflector. The position of the retroreflector isdetermined by the laser interferometer (radial distance) and the laserbeam direction (two angles) as in a polar coordinate system. W. F.Marantette uses a machine tool position measurement employing multiplelaser distance measurements; U.S. Pat. No. 5,387,969, granted Feb. 7,1995 discloses three laser interferometers and a scanning mirror deviceto point the laser beam to the retroreflector. The spindle position in aplane is determined by the measurements of the two laser interferometersusing the formula of triangulation. However, these systems are verycomplex and less accurate than the present invention.

Another inferior technique in one used by J. C. Ziegert and C. D. Mize(measurement instrument with interferometer and method) as disclosed inU.S. Pat. No. 5,428,446 granted Jun. 27, 1995. It discloses the use of alaser interferometer to replace the linear transducer in a telescopingball-bar gauge.

Since a laser interferometer is more accurate and longer range than alinear transducer, the measurement range becomes larger. Hence, it ispossible to measure non-circular tool paths, and the spindle positioncan be determined by trilateration. However, it cannot be used tomeasure small circles and it is also very expensive.

Thus, the ball-bar and other prior techniques for making dynamic toolpath measurements are either inaccurate, incomplete, time consuming, orextremely costly relative to that achievable with the present invention.

III SUMMARY OF INVENTION

Briefly, conventional laser interferometers using a retroreflector asthe target mounted on the machine tool spindle can measure the lineardisplacement relative to a single axis thereof accurately. However, thetolerance for lateral displacement is rather small. Using preferably asingle-aperture (or less desirable modified prior art two-aperture)laser target displacement measuring system like the Laser DopplerDisplacement Meter (LDDM) of Optodyne, Inc. of Compton Calif. and alarge flat-mirror or unusually large retroreflector as the target, thelinear displacement along the laser beam direction can be measured withlarge tolerance on lateral displacement under small angular shifting ofthe target. This angular shifting problem can be minimized using aunique diverging laser beam when a flat-mirror target is used as shownin FIG. 3.

Using three such laser systems, pointing their laser head beams at 90degree to each other, namely in the X, Y and Z axis directions, withpreferably three flat-mirror targets perpendicular to the three axesrespectively, the xyz-coordinate displacements of the target trajectorycan be measured simultaneously. While it is preferred to place the flatmirrors on the spindle with the laser heads mounted on a stationarysurface, the present invention also envisions reversing the positions ofthe laser heads and flat mirrors.

However, a preferred specific aspect of the present invention whichreduces the equipment cost considerably to the customer is to use onlyone such system where the preferably stationary laser head thereof issequentially directed along each of these axes to make threesequentially taken target displacement measurement sequences. This lesscostly system is only useable when the target positions can be repeatedin sequence exactly, which is usually the case. In such case, three flatmirrors are preferably placed on the spindle facing in the directions ofthe three axes, or one flat mirror designed to be mounted sequentiallyon three different axially facing sides of the spindle are so placed,before each measurement sequence is taken. (As above indicated, thelaser head and mirror locations can less desirably be reversed so thatthe laser head is mounted on the spindle target sequentially ondifferent sides thereof and one or three mirrors are mounted on astationary surface facing in the three directions to intercept the laserhead beams.) In this form of the invention, a means is provided tosynchronize the three sets of sequentially taken data so that themeasurements for the corresponding positions and data sampling times ofthe target are related. This can be done in a number of ways, one bystarting the data sampling times as the target is at the same pathposition when target position sampling begins. Another way is to programthe tool path to do a “spike”motion, for example, a rapid back and forthmotion along a 45 degree direction between the axes involved.

The invention provides data collection, storage, computing,synchronizing and outputting processing means which supplies and storesinformation on the deviation of the actual from the programmed target(e.g. the machine tool spindle) positions for each sampled X, Y or Zaxis position of the target and preferably also from the actual desiredpath thereof. Thus, these means have stored therein digital datarepresenting the desired positions of the target along the various axesfor the various target position sampling times involved and this desiredtarget position data is compared with the corresponding actual measuredaxis target position data involved. The resulting axis position errornumbers for each sampled target path position along each axis are storedfor printout as path deviation numbers for each desired path positioninvolved.

In accordance with another aspect of the invention, the data outputtingmeans outputs the data to a printer or plotting means which displays twosets of overlaid lines, one representing the desired target path and theother the actual path in a manner where the degree of deviation isreadily visible. Usually the deviations between the actual and desiredtarget paths are so small that these differences are not visible on theoverlaid lines. This problem is overcome by multiplying the axisdeviation numbers by as much as a thousand or more times, adding themultiplied numbers to the desired target position numbers along the axesat the sampling times involved and then displaying on a printer orplotting device the modified actual and programmed position-indicatinglines together.

If the target trajectory is to be only a circle in one plane, it isespecially desirable to store the path deviation numbers for eachsampling time for number printout in polar (i.e. angular) as well asaxial terms. Thus, the polar deviation error for a particular targetposition along the circular path involved is computed from the X and Yaxis position error numbers involved by computing the square root of thesums of the squares of these numbers. Also, when the target path is tobe a circle in one plane, the sequentially taken data can besynchronized easily even when the X and Y axis related data taken at thesame sampling rate starts with the target at different path positionpoints. Thus a circular path is generated and displayed bysimultaneously combining the data taken along the two axes, with themaximum or minimum displacement data taken along one axis correspondingin time to the mean (half-way between minimum and maximum) values of theother. The waveforms of such data is a sine-like curve representing theposition data for one axis and a cosine-like curve representing theposition data for the other axis when the sampling times are equallyspaced periods.

The tool path R for any path configuration can be expressed as:

Ri(Xi,Yi,Zi), i=1,2, . . . N  (1)

Where Xi, Yi and Zi are data collected with laser system #1, #2 and #3,respectively and simultaneously where three systems are used or when onesystem is used sequentially as described. Once the phase relation ofthese three sets of data is determined as just described, the tool pathRi are determined by substituting these three sets of data into Eqn. 1.This composite tool path may be deviated from the tool path measured by3 laser systems simultaneously if the tool path is not repeatable andthe velocity of the motion is not constant. The effect of non-repeatableand non-uniform velocity of the motion can be minimized by collectingdata over several cycles and using the mean values.

Similarly, for a complete 6 degree spindle motion, x, y, z, pitch, yaw,and roll, 6 laser systems can be used to measure the tool path Ri(Xi,Yi, Zi, X′i, Y′i, Z′i). The pitch angle is (Xi−X′i)/d, where d is thebeam separation. The yaw and roll angles are (Yi−Yi′)/d and (Zi−Z′i)/drespectively.

IV. DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic showing a double-path parallel beam opticalarrangement of a laser system useable in the present invention andutilizing an unusually large retroreflector facing a laser head toreflect its beam against a stationary flat mirror even when theretroreflector or the laser head is moved appreciably away from themeasuring axis involved.

FIG. 2 is a schematic showing a double-path un-parallel beam opticalarrangement of a laser measuring system where a flat mirror mostadvantageously mounted on a machine tool spindle opposite and at anangle to a laser beam directed from the laser head reflects the beamtoward a stationary retroreflector much smaller than that shown in FIG.1 and facing the flat mirror reflected beam. As compared to the FIG. 1arrangement, the FIG. 2 system, while simpler to setup than the FIG. 1system, is undesirably more sensitive to unwanted spindle tilt and theuseable measurement range is much shorter than that for the FIG. 1system.

FIG. 3 is a schematic showing a single-path laser system useable in thepresent invention, the system using a preferably stationary laser headwith a beam-spreading lens system directing the diverging beam to a flatmirror preferably mounted on the machine tool spindle. As compared tothe FIG. 1 arrangement, it is somewhat more undesirably sensitive to theunwanted tilt of the machine tool spindle and the range of themeasurement is shorter by about 10 to 20 inches. However, for mostmachine tools with working volumes of 40″×20″×20″, this is the preferredlaser system of the invention.

FIG. 3A shows a commercially available double-aperture laser head 1Bwith a modified optical arrangement using a flat mirror 9 as the target.

FIG. 4 is a schematic showing two single-aperture laser heads mounted ona stationary surface pointing their beams in the X-direction andY-direction respectively, and two large flat mirrors mounted on amachine tool spindle, the motion of the spindle being measured by thetwo laser systems simultaneously.

FIG. 5 is a schematic showing two single-aperture laser heads mounted ona spindle with one laser head pointing its beam in the X-direction andanother laser head pointing its beam in the Y-direction and two flatmirrors mounted on the machine bed respectively perpendicular to the twolaser beams, the motion of the spindle being measured by the two lasersystems simultaneously.

FIG. 6 is a schematic showing a 3-dimensional laser measuring systemlike the two-dimensional system of FIG. 4, but with a third laser headand a third flat mirror added on the machine pointing in thez-direction.

FIG. 7 is a schematic showing a 3-dimensional FIG. 1 type measuringsystem similar to FIG. 5, but with a third laser head mounted on thespindle and a flat mirror added on the machine bed pointing in theZ-direction, the motion of the spindle being measured by the three lasersystem simultaneously.

FIG. 8 is a block diagram showing three of the laser heads involvedpointing their beams respectively in the X-direction, Y-direction andZ-direction. (If one system is used sequentially as previouslydescribed, then the three laser heads shown represent the one systemsequentially positioned to direct its beam parallel to thesedirections.) FIG. 8 also shows a block representing portions of a PC orother data collection and processing system involved which collects,stores, computes, synchronizes, and outputs the computed position errordata to a printer or curve plotter there shown.

FIG. 9A is a schematic showing in solid lines a flat mirror mounted on amachine tool spindle in a (0 degree) position A, the spindle to beideally moved clockwise 360 degrees in a circular clockwise path having90, 180, and 270 degree positions represented respectively by referencecharacters B, C and D. (The 360 degree position is also shown byreference character A.) FIGS. 9B and 9C drawn respectively below and toone side of the laser system of FIG. 9A represent respectively thedesired X and Y axis spindle displacement verses time curves oriented at90 degrees to one another for the various assumed equally spacedsampling times involved, and show the X and Y axis data starting atrespectively different random starting times T(S) and T(S)′, the timesT(A,), T(B,D), and T(C) and T(D)′, T(C.A)′ and T(B)′ being respectivelythe random times when the spindle is programmed to be at the minimum,medium and maximum X and Y axis displacement points.

FIGS. 10A and 10B are the X and Y axis displacement verses sampling timecurves of FIGS. 9B and 9C drawn to a horizontally oriented time basewhen the time axes start at times T(S) and T(S)′. FIG. 10C shows the Yaxis displacement curve shifted (i.e. synchronized) so that the minimum,median and maximum x axis displacement points of the X axis data curveare opposite the median, maximum and minimum points of the mediumdisplacement points of the Y axis data curve as they would be if suchdata were taken at the same rather than at different sequential randomstarting times.

FIG. 11 shows an ideal circular curve representing the desiredprogrammed spindle displacement overlapped by an imperfect circular plotshowing the various deviations of the actual measured spindle positionsfor the corresponding polar positions of the spindle, but with thedeviation amounts multiplied by a factor of about 1000 so that thedeviations from the actual and desired circular path can be seen.

FIG. 12A is a block diagram showing the broad program routine sequencesused to do a circular test in the XY-plane as shown in FIG. 11, using asingle laser system sequentially to measure the spindle movements alongthe X and Y axes.

FIG. 12B show a much more detailed block diagram showing the moredetailed program steps performed by the program involved than that shownin FIG. 12A.

FIG. 13 is a block diagram like FIG. 8, but showing in block form usingadditional blocks to illustrate the functions carried out by the blocks102 and 106 in FIG. 8, when the present invention is practiced usingonly one laser head sequentially positioned to direct its beam along theX and Y axes to determine and display a circular target path error.

V. DETAILED DESCRIPTION OF THE ILLUSTRATED EMBODIMENT

The double-path parallel beam laser system shown in FIG. 1 consists of asingle-aperture laser head 1A, an unconventionally large retroreflector2 and a flat-mirror 3. (For example, the retroreflector could be aslarge as 10″ inches in diameter.) The laser head's output laser beam 4is first reflected by the large retroreflector 2 to produce a firstreflected beam 5 parallel to but displaced from output beam 4. The flatmirror 3 is perpendicular to the first reflected beam 5, hence the flatmirror-reflected beam 6 coincides with the first reflected beam 5, butin the opposite direction. The latter beam 6 is reflected again by thelarge retroreflector 2 to form return beam 7 which coincides with outputbeam 4 but in the opposite direction and is returned to the single laserhead aperture. It is noted that the property of the retroreflector 2 isthat the incident beam direction and the reflected beam direction areparallel and in the opposite direction. This property is not affected bythe location and angle of the incident laser beam. Also, if theretroreflector 2 is moved perpendicular to the output beam 4, the firstreflected beam 5 will move to a different position on the flat mirror 3.However, the position of the return beam 7 will not change and the totalpath length from laser head to the flat mirror due only to thisperpendicular movement remains the same. Therefore, the displacementmeasured is in the beam direction parallel to the X-axis shown. TheX-axis measurement also will not be effected by any retroreflectormovements perpendicular to the other (Y and Z) axes.

The laser head 1A and similarly identified laser heads shown in FIG. 1and the other drawings are preferably, but not necessarily,single-aperture, single beam laser heads made and patented by Optodyne,Inc. of Compton Calif. U.S. Pat. No. 5,116,126 discloses one suchOptodyne laser head which, as do others, provide an accurate measure ofthe distance between a preferably laser beam source and a reflectoropposite the beam source. One of the beam source and reflector ismounted on a target, such as a machine tool spindle, and the other on astationary surface, like a machine tool bed. Other reflectors, inaddition to the one opposite the beam source, such as those to be hereindescribed. (Also, other but less desirable beam energy targetdisplacement measuring systems may be used in accordance with thebroadest aspects of the invention.)

FIG. 2 illustrates a double-path angular reflected laser beam systemproducing unparallel output and first reflected beams which can be usedin the present invention. FIG. 3 of Optodyne U.S. Pat. No. 5,394,233shows such a laser beam system. This system comprises a single-aperturelaser head lA, a large flat mirror 9 directed at an angle to the outputbeam 11 and a preferable normal sized retroreflector 10 (to minimizesystem cost) much smaller than the reflector 2 in FIG. 2 and facing thebeam 12 first reflected from the retroreflector 10. The output laserbeam 11 is reflected by the flat mirror 9 towards the retroreflector 10.The first reflected beam 12 is reflected back by the retroreflector 10towards the flat mirror 9 which produces a reflected return beam 14received by the aperture of the laser head 1A.

Since the output and return beams 11 and 14 are not parallel to thereflected beams 12 and 13, when the flat mirror 9 moves forward orbackward relative to the laser head 1A the return beam 14 is stillparallel but shifted from output beam 11. The amount of the shift isinversely proportional to the angle between beams 11 and 12. Hence themeasurement range is longer for smaller angles or larger initialflat-mirror to laser head spacing. For example, the retroreflector 10 isplaced very close to the laser head 1A. For a 5 mm diameter laser beam,the range is about +/− 20% of the distance between the laser head 1B andthe flat mirror 9. Also because of the double-path and the (cosine) beamangle involved, the laser reading is increased by the factor2*Cos(theta), where 2 is for the double-path and theta is the anglebetween beams 11 and 12. Also, when the flat mirror 9 is moving in theY-direction perpendicular to the illustrated X-axis measurementdirection, the measurement reading of X will show Y*Sin(theta). Hence itis important to keep the angle theta small.

As in the FIG. 2 and other embodiments of the invention using tworeflecting mirrors, the mirror used to reflect a beam directed to itfrom the reflector first receiving the laser head beam and the laserhead involved can both be mounted together on a stationary surface or onthe target (e.g. machine tool spindle) and the mirror which firstreceives the laser head beam can be mounted on the other of same.

FIG. 3, illustrates a single aperture, single path laser measurementsystem with a large flat mirror 18 facing the laser head 1A as thetarget. A lens system 16 placed adjacent to the laser head apertureconverts the collimated beam of the laser head to a divergent outputbeam 17. The output laser beam 17 is reflected by the flat mirror 18 andreturned to the laser head 1A through the lens system 16. Because thebeam is divergent, the laser beam should return to the receivingaperture even when the flat-mirror 18 is undesirably tilted a smallangle (less than one half of the beam divergence angle). Since thetarget is a large flat mirror 18, any displacement perpendicular to theincident laser beam 17 or parallel to the mirror surface will not changethe path length from the laser head 1A to the flat mirror 18. Therefore,the displacement measured is in the beam direction only so that themeasurement will not be affected by any displacement perpendicular tothe beam direction. However, this assumes that the flat mirror isperpendicular to the laser beam 17. Any small tilt angle theta willcause a lateral coupling of Y*Sin(theta) or Z*Sin(theta).

FIG. 3A shows a commercially available double-aperture laser head 1Awith a modified optical arrangement using a flat mirror 9 as the target.The output laser beam 20 a is reflected by the flat mirror target 9 as areturn beam 20 b back toward the exit aperture of the laser head 1B. Abeam splitter means 18 then reflects downward as viewed in FIG. 3A halfof the return beam 20 b toward an angular directed fixed highreflectivity mirror 20 c which reflects the beam to produce a returnbeam 209 to the second receiving aperture of the laser head 1A.

FIG. 4 illustrates a two-dimensional laser measurement system using twolaser heads 1A-1 and 1A-2 and accompanying beam-diverging lens systems16 as shown in FIG. 3 mounted on a stationary surface. Here two flatmirrors 30 and 33 mounted on a machine tool spindle 31 are positioned toface in two different orthogonal directions along which are directed theoncoming diverging beams emanating from the lens systems 16. Hence the2-dimensional displacement of the spindle 31 can be measured by thelaser heads 1A-1 and 1A-2 simultaneously. The range of the spindledisplacement is limited by the size of the flat mirrors 30 and 33.

FIG. 5 illustrates a similar two-dimensional laser measurement systemwhere the similarly oriented mirrors 36 and 38 are shown mounted onstationary surfaces, such as on the machine tool bed, and the laserheads 1A-1 and 1A-2 are mounted together and parallel to each other.Their associated beam diverging lens systems 16 and 16′ are mounted onthe machine tool spindle 31. The lens system 16 is the same as thatshown in FIG. 3 and directs a divergent beam 35 horizontally as viewedin FIG. 5, whereas the lens system 16′ directs a divergent beam 37 beamin a downward direction as viewed in FIG. 5. The range of the spindledisplacement is only limited by the size of the flat mirrors 36 and 38.For 12″ size flat mirrors, the spindle is limited to move within a 12inch range relative to each axis. Similarly, if one more laser system isadded to that shown in FIG. 4 or FIG. 5, 3 dimensional spindle tool pathdisplacement can be measured along the three axes simultaneously, asshown also in FIGS. 6, and 7.

FIG. 6 illustrates a 3-dimensional laser measurement system using threelaser heads 1A-1, 1A-2 and 1A-3, like that shown in FIG. 3 (althoughthey could be other beam sources as, for example, like those shown inFIGS. 1 or 2). The laser heads are shown and mounted on the machine toolbed directing their beams 40, 43 and 45 simultaneously respectivelyalong the X, Y and Z axes of the tool path movement space toward threeflat mirrors 30, 34 and 33. These mirrors are mounted on the machinetool spindle 31 so as to face the respective oncoming laser heads beams40, 43 and 45. The outputs of the laser heads shown in this Figure andin FIG. 4, if they are produced by said Optodyne laser heads are binarysignals which indicate the various X, Y and Z axis positions of thetarget involved. Timing signals generated by the processing means towhich the laser head outputs are fed store the target positions at thesampling times involved.

FIG. 7 illustrates a 3-dimensional laser measurement system similar tothe two-axis system of FIG. 5, but with one additional laser headmounted on the spindle 31. The three laser heads appear as a singlehousing assembly 46. The assembly 46 has laser beam-diverging lenssystems 16 and 16′ at the bottom thereof directing diverging beams 51and 49 along the horizontally directed X and Y axes toward flat mirrors48 and 50 mounted on the machine tool bed 54. The third laser headforming part of the assembly 46 directs a diverging beam downward in theZ axis direction onto a mirror 52 mounted on the top surface of the bed54.

The FIG. 6 and FIG. 7 embodiments could be modified so that any of thevarious combinations of positions of the laser heads and flat mirrorscould be used. Thus the spindle could carry one or two instead of threeflat mirrors or one or two instead of three laser heads.

FIG. 8 is a block diagram showing three of the laser heads 1A-1, 1A-2and 1A-3 involved pointing their beams respectively in the X-direction,Y-direction and Z-direction upon mirrors carried on the spindlerepresented by box 31. (If one system is used sequentially as previouslydescribed, then the three laser heads shown represent the one systemsequentially positioned to direct its beam parallel to thesedirections.) FIG. 8 also shows blocks 104 a and 104 b representingrespectively a printer and line plotter and a box 102 representing theprocessing portion of a PC or other data collection and processingsystem involved which collects, stores, computes, synchronizes, andoutputs the computed position error data to the printer 104 a and/orcurve plotter 104 b.

More specifically, some of the functions performed by the dataprocessing means represented by the box 102 are: (a) the conversion,storing and arranging, when necessary, of the X, Y and Z axisdisplacement-indicating information fed from the laser heads to binaryand digital form for the various equally time-spaced sampling times whenmeasuring data is taken so that the X, Y and Z axis data for the varioussampling times is identified; (b) the computing and storing for futureprintout of the path error differences between the desired and actualposition of the spindle relative to each of the axes involved at thevarious corresponding sampling times; (c) the multiplying and storing ofthese multiplied difference values if a visual overlapping line plot ofthe desired and actual spindle path positions as shown in FIG. 11 for acircular path; (d) the addition of the multiplied position error valuesto the stored data representing the ideal path positions for thesampling times involved; (e) the conversion of the various multipliedaxis error values to polar values when a circular path is involved; and(f) the feeding of signals to the printer 104 a or plotter 104 b to readout the path error data in axial or polar error-indicating form. Where acircular line plot is desired the processing means 102 would generatesinusoidal and co-sinusoidal-like voltages representing the desired andactual spindle movements for feeding to a line plotter requiring suchvoltages.

FIG. 8 also shows a box 106 identified as spindle moving means whosecomponent parts are shown in more detail in FIG. 13 which also showsindividual blocks showing storage and program elements which respond tothe stored position data to generate the various signals fed to theprinter and plotter where the target is moved only in a circular path.

FIG. 9A illustrates a circular path error test using only one laser head1A to sequentially positioned to direct its beam along the X and Y axeswhere target position measurements are taken without concern for theposition of the target when a measurement sequence begins and is takenat predetermined sampling rate. In the system there illustrated, thelaser head 1A mounted on a stationary surface has a beam-diverging lenssystem 16 directing a beam 63 to a flat mirror 65 mounted on a machinetool spindle to be moved in a clockwise circular path. The X-axisdirected output diverging laser beam 63 is shown reflected by the flatmirror 65 and returned to the laser head 1A as a return beam 64. Becausethe beam is divergent, the laser beam should return to the laser headreceiving aperture even when the flat mirror 65 is undesirably tilted bya small angle. The reference characters A, B C and D in FIG. 9A show theflat mirror-carrying spindle positions at the 0, 90, 180 and 270 degreepositions of the desired circular path involved. The output beam 63 isalways reflected back as beam 64 by the flat mirror 65 at the A, B, Cand D and the positions therebetween. After measurements are taken atthe selected sampling times with the beam directed along the X axis,

To complete the circular path test, the laser head 1A is moved to pointwhere it directs a divergent beam parallel to the other or Y axisinvolved. The flat mirror 65 can be designed to be remounted on thespindle 31 to be perpendicular to the Y axis directed laser beam.Another set of measurements at the same sampling rate are then taken asthe spindle is moved again in the same preferably repeatable circularpath. By combining the data taken along the X and Y axes, circular toolpath indicating signals can be generated and fed to a printer or plotterto draw the ideal and actual circular path movements.

In the explanation of the circle test now to follow, the times whenrandom measurement of spindle position along the X-axis begins will beindicated respectively by T(S) and T(S)′. The random times when thespindle reaches the A, B, C and D positions on the circular pathinvolved for the X and Y axis measurements will be indicatedrespectively by T(A), T(B), T(C) and T(D) and T(A)′, T(B)′, T(C)′, andT(D)′.

FIGS. 9B and 9C drawn opposite FIG. 9A represent respectively the actualX and Y axis spindle displacement verses time curves oriented at 90degrees to one another for the various assumed equally spaced samplingtimes involved, and show the X and Y axis data starting at respectivelythe different random starting times T(S) and T(S)′, Note that at thetimes T(A), T(B), and T(C) and T(A)′, T(B)′ and T(C)′ representing thetime during the sequential measurements when the spindle is programmedto be at the circle positions A, B, C and D that the X axis measurementsare respectively at their minimum, median (i.e. half way between theirminimum and maximum values), maximum and median X axis displacementpositions and the Y axis measurements are respectively at their median,maximum, median and minimum Y axis displacement positions. FIGS. 9B and9C so indicate as they also indicate that relative to the datacollection starting times T(S) and T(S)′ the collected data at timesT(A)−T(A)′, T(B)−T(B)′, T(C)−T(C)′ and T(D)−T(D)′ do not occur at thesame times relative to the starting times. In order to be able to outputsignals to the printer or plotter which will draw circular lines thecollected data must be related so that the stored measurement issynchronized or repositioned in storage so that the corresponding A, B,C and D position data is located at the same time slots relative to thestart measurement times T(S) and T(S)′. This synchronizing process isillustrated in FIGS. 10A, 10B and 10C.

Accordingly, FIGS. 10A and 10B are the X and Y axis displacement versessampling time curves of FIGS. 9B and 9C drawn to a horizontally orientedtime base when the time axes start at times T(S) and T(S)′. FIG. 10Cshows the Y axis displacement curve shifted so that the minimum, medianand maximum X axis displacement points of the X axis data curve areopposite the median, maximum and minimum Y axis displacement points, asthey would be if such data were taken at the same rather than atdifferent sequential random starting times.

FIG. 11 shows an ideal circular curve representing the desiredprogrammed spindle displacement overlapped by an imperfect circular plotshowing the various deviations of the actual measured spindle positionsfor the corresponding polar positions of the spindle, but with thedeviation amounts multiplied by a factor of about 1000 so that thedeviations from the actual desired circular path curve can be seendisplaced from the desired curve where displacement errors exist. Theresult of this multiplication operation is added to the correspondingdesired displacement data. The thus modified and synchronized actual Xand Y axis position data is converted to corresponding X and Y axis dataanalog signals and fed to a plotter which receives such analog signalsto draw the actual position curve shown in FIG. 11. A printer whichreceives digital data can be programmed to do the same thing digitallyso that the digital printer prints or draws lines representing thedesired circular and near circular path position lines like that shownin FIG. 11.

FIG. 12A is a block diagram showing the broad program routine sequencesused to do a circular test in the XY-plane as shown in FIG. 11, using asingle laser system sequentially to measure the spindle movements alongthe X and Y axes;

FIG. 12B shows a much more detailed block diagram showing the detailedprogram sub-routines of the boxes in FIG. 12B. Thus, FIG. 12B showsblocks or boxes numbered 102 followed by different alphabet charactersa-h and some with primes (′) thereafter represent the various means ofthe software and/or hardware involved which perform the functionsidentified in each of the boxes shown. The box labeled 102 in FIG. 8includes all of these means now to be described. Accordingly, boxes 102a and 102 a′ identify the means which input the binary data developed bythe X and Y axis laser heads to a data file; boxes 102 b and 102 b′identify the means which converts this binary data to Ascii file (i/e/digital) data; and common box 102 c are the means which synchronizes orre-arranges this data so that the maximum, means and minimum values ofthe Xdata is opposite or corresponds respectively to the mean, minimumand maximum values of the Y data.

The re-arranged X and Y axis actual object spindle data outputted by themeans represented by the common box 102 c is fed to the meansrepresented by the boxes 102 d and 102 d′ labeled “Compute and store Xdata” and “Compute and store Y data” for each position. As previouslyindicated, these functions preferably include a subtraction and storingoperation where the actual X and Y axis error value for each spindleposition is indicated in memory. The output of boxes 102 d and 102 d′are shown fed to a box 102 f labeled “Compute and store polar error”.This box represents the function of computing the square root of thesquares of the X and Y axis data so that the actual angular or polarerror for each spindle position is recorded.

The next box 102 g shown fed by the output of boxes 102 d and 102 d′ islabeled “multiply X-Y position error and add to desired date”. Thus,this box represents the function performed by the means which multipliesby about 1000 or more in most cases the X and Y axis error data for eachspindle position and adding the multiplied data to the correspondingdesired programmed position value for each position involved. The outputof box 102 g as shown fed to the next box 102 h labeled “Printsequentially desired and modified actual displacement circles” whichcarries out the function of outputting signals to the printer or plotterinvolved to display the perfect and imperfect circular lines shown inFIG. 11.

FIG. 13 is a block diagram like FIG. 8 but showing in block form more ofthe functions carried out by the data collection, storage and processingmeans shown as a single block 102 in FIG. 8, and wherein a single laserhead is used sequentially as described to obtain X and Y axis data to besynchronized, compared, multiplied and then fed to a printer or plotterto draw the overlapping curves of FIG. 11.

FIG. 13 thus has blocks or boxes namely: boxes 102-1 and 102-1′identified respectively as X and Y axis actual position storage meanswhich store the actual X and Y axis object position data; boxes 102-2and 102-2′ identified respectively as X and Y axis desired positionstorage means which store the desired programmed X and Y axis objectposition data for the various assumed object positions for which theactual position data was taken; boxes 102-3 and 102-3′ coupled to theoutputs of the latter boxes and respectively identified as X and Yposition comparison and multiplying means which subtracts the desiredand actual position data for each of these positions to determine andstore the position error and then multiplies the error computations andstores the same; box 102-5 identified as the synchronizing and timingmeans which controls the timing of the functions performed by theaforesaid boxes; a box 104 identified as a synchronizing and timingmeans; boxes 102-4 and 102-4′ respectively identified as X and Y axissine and cosine signal generating means coupled to the outputs of thelatter boxes; 102-1, 102-1′, and 102-3 and 102-3′ to generate the sineand cosine signals which when fed to a curve plotting means shown as box104 b will plot circular or circular-like curves as shown in FIG. 11;printing and curve plotting means; and a dashed box 106 which has boxesidentified as X and Y axis movement programming means 106 a and 106 a′coupled to the inputs of boxes 106 b and 106 b′ respectively identifiedas sine and cosine voltage generating means shown coupled respectivelyto X and Y axis motors 106 c and 106 c′ which control the movement of amachine tool spindle 31. FIG. 13 also shows a box 104 a representing aprinter means which receives signals from the X and Y positioncomparison and multiplying means 102-3 and 102-3′ to print circle-likecurves from the data stored therein.

For a more general analysis of the operation of the present invention toany two or three dimensional tool path measured by 2 or 3 laser systems,as in the case of the two-dimensional circular path measurement systemjust reviewed, the data actual target position data is collected at afixed data rate and synchronized by latching all three data measurementsto the same time base (within a small electronic delay time). The toolpath R can be expressed as . . .

Ri(Xi,Yi,Zi), i=1.2, . . . N  (2)

where Xi, Yi and Zi are data collected with laser #1, #2 and #3respectively. Assume the programmed tool path is

 rj(xj,yj,zj), j=1,2, . . . M  (3)

First, take two reference points from the programmed tool path and thetwo corresponding points on the measured tool path. Translate thecoordinate system in the measured tool path such that the firstreference point r (ref 1) in the programmed tool path coincide with thefirst reference point R (ref 1) in the measured tool path. That is

r(ref 1)=R(ref 1)  (4)

The second reference point is used to check the scales and the angle ofthe coordinate systems between the measured tool path and the programmedtool path.

For a 2 dimensional tool path, plot both the programmed tool path r andthe measured tool path R on the same graph and compare the differences.

For a 3 dimensional tool path, we can project the 3 dimensional toolpath to three 2 dimensional tool paths and compare the differences ofeach 2 dimensional tool paths.

If the differences are very small, the tool path differences D=/r−R/ canbe calculated along the normal of the programmed tool path.

For most CNC Machines, the tool paths are very repeatable. It ispossible to use only one laser system but measures three times, inX-direction, Y-direction and Z-direction respectively. The three sets ofdata collected should be the same as the three sets of data collectedsimultaneously, except the phase relations between these three sets ofdata have to be determined. The phase relations can be determined byeither using an external trigger signal at the same location, or byusing a sharp turn on the same location as a marker. Once the phaserelations between the three sets of data are determined, the tool pathRi can be generated by the measured Xi, Yi, and Zi.

For example, as shown in FIG. 9A, pointing the laser beam in theX-direction and mounting the flat-mirror target on the spindle, theX-coordinate of the spindle motion can be measured even with largeY-direction movement. By repeating the measurement in the Y-direction,the Y-coordinate of the spindle motion can be measured. Assume thespindle motion is repeatable to certain tolerance, the data onX-coordinate and Y-coordinate can be combined to generate the circularspindle path. As shown in FIGS. 10A, 10B and 10C, the measurement datain the X-direction and in the Y-direction can be combined to generatethe circular path. Since the actual tool path is not a perfect circle,the curve as shown are not perfect sine or cosine functions. Hence thecombined circular path is not a perfect circle. The deviation from aperfect circle can be calculated and plotted in FIG. 11. The maximumdeviation larger than the perfect circle is the Fmax, the maximumdeviation smaller than the perfect circle is the Fmin, and the meandeviation from the perfect circle is the circularity.

The following are the actual test conditions for the FIG. 11 plot:

Measuring plan: XY

Direction: X and Y

Feedrate: 20 in/minute

Sampling rate: 30′ sec

Rotation sense: CW

Radius: 2 in.

Starting point: X=20 in

Y=10 in

Distance from target: 30 in

Measuring radius: 2.000092 in

Circularity: ±).000112 in rms.

Radial deviation:

Fxy, max=+0.000352 in

Fxy, min=−0.000282 in

The composite tool path can be used to compare the programmed tool pathas discussed previously. Of course, the accuracy of this composite toolpath is limited by the repeatability of the tool paths and the speedfluctuations of the tool paths. To minimize these effects, it ispossible to measure the tool path over several cycles and use the meanvalue as the measured tool path.

In summary, most CNC Machines are very repeatable, Hence, using only onelaser system, the tool path in 2 or 3 dimensions can be measured.

The most important, but not the only, application of the invention isthe one described above where the invention determines the accuracywhich a machine tool or the like moves an object in a path where theredesirably would not be any angular or rotational motion between the beamdirecting means and the reflector which first receives the beam.However, the invention in its broadest aspects is also applicable inproviding a measure of the accuracy of the object moving apparatusinvolved where the object is desirably to be rotated or pivoted so thatthe object is to have a desired pitch, yaw and roll motion in additionto an X, Y and Z axis motion. To measure object movement error for allof these motions would require 6 laser measuring systems or operations.In other words, the object measuring operations would require three suchsystems operated simultaneously as described above to measure the X, Yand Z axis motion accuracy (or one such system operated sequentially asabove described) and three more such systems (or one more operatedsequentially three more times) to collect the data necessary to computethe pitch, yaw and roll error (resulting from the movement of the objectalong the same path as before but with the desire pitch, yaw and rollmotions imparted to the object at the same path positions the object hadduring the axial error path determining measurements.) The latter errorcomputations require error computing equations different from those useddescribed above in the X, Y and Z axis error application of theinvention.

Accordingly, the claims are intended to cover all of these applicationsof the invention. The laser measuring system of FIG. 1 using a largeretroreflector as shown is the preferred measuring system for theapplication of the invention for determining the pitch, yaw and rollerror data. For this application of the invention, the position errordata is collected in the same way as above described for measuring X, Yand Z axis error as the object being moved is moved along the same pathbut with pitch, yaw and roll components of motion added to the axialcomponents of motion. although the data processing functions aredifferent due to the different equations needed to compute the pitch,yaw and roll error involved.

While, the simple large retroreflector shown in FIG. 1 is the preferredretroreflector, the one shown could be replaced by a corner cube, solidprism, cat-eye or other type of retroreflector.

VI. SOME MAJOR FEATURES OF THE INVENTION

Summaries of some of the features of the invention are as follows:

1. A technique to measure the 3 dimensional, or 2 dimensional tool pathswith laser interferometers or LDDMs using the single-aperture lasersystems and double-path optical arrangements.

2. A technique to measure the 3 dimensional, or 2 dimensional tool pathswith laser interferometers or LDDMs using a lens-systems andflat-mirrors.

3. A technique to measure the 3 dimensional, or 2 dimensional tool pathswith only one laser unit but repeated measurements.

4. A technique to synchronize the data of repeated measurement byexternal trigger signal and to combine the measured data to generate a 3dimensional or 2 dimensional tool path.

5. A technique to combine the separately measured data to generate a 3dimensional, or 2 dimensional tool path using specially programmed toolpath at locations as marker.

6. Circular test or telescopic ball-bar test with a laser system, a lenssystem and a long flat-mirror.

7. Mirrors applied as position feedback to control the spindle positionor the position of a 3 dimensional stages.

8. The use in the above technique of a divergent beam to reduce analignment problem.

I claim:
 1. A system for determining the degree of accuracy an object ismoved along a given path in a space having at least two orthogonal axesby object moving apparatus having a different motor for imparting objectmovement relative to said respective axes to produce an overall objectmovement path, said apparatus having programming means having stored inthe memory thereof desired object path position data relative to saidaxes at various reference times, and means responsive to said desiredpath position data for generating motor-energizing signals for saidrespective motors to desirably move said object along said desired path;said system comprising: one or more beam directing means for directing abeam of energy simultaneously parallel respectively to said axes if morethan one such means is provided or parallel to one of said axes at atime if only one such means is provided and its beam is to besequentially directed parallel to said orthogonal axes, at least onebeam reflecting means associated with each beam directing means and tobe positioned to directly receive the beam from its associated beamdirecting means, at least one of each of said beam directing means andsaid at least one reflecting means associated therewith being mountableon said object and the other being mountable on a relatively stationarysurface, said at least one reflecting means associated with each beamdirecting means being sufficiently large to reflect such directed beamto ultimately return the beam to said beam directing means even as theobject is moved in a desired path which deviates from the direction inwhich the beam involved is directed; and signal processing meansincluding means responsive to the return of each reflected beam ofenergy to the associated beam directing means for developing actualobject path position data indicating the actual displacement of saidobject relative to said axes at sampling times coincident with saidreference times; and additional processing means including datacollection, storage, comparing and data outputting means for collectingand storing said desired and actual object path position data relativeto said axes at said reference and sampling times, and for comparing thestored desired and actual position data at said reference and samplingtimes and indicating the degree of position error relative to said axesat said sampling times.
 2. The system of claim 1 wherein said at leastone reflecting means associated with each beam directing means is a flatmirror.
 3. The system of claim 2 wherein the associated beam directingmeans includes lens means for directing a diverging beam to said flatmirror.
 4. The system of claim 1 where there is provided a separate beamdirecting means for each axis so that three beams can be simultaneouslydirected along each of said axes, simultaneously to collect said actualobject position data.
 5. The system of claim 1 wherein there is providedonly one of said beam directing means to direct a single beamsequentially when re-positioned to do so parallel to said variousorthogonal axes as said object moving apparatus repeats the movement ofsaid object along a supposed desired path, to sequentially develop saidactual object path position data relative to said respective axes, andsaid processing means including synchronizing means for relating theactual object position data relative to said respective axes taken intime sequence at said sampling times to the same positions of saidobject along its path of movement.
 6. The system of claim 5 used tocollect and process object position data where the object is to bedesirably moved in a circular path in a given plane having twoorthogonal axes and where said single beam source is to direct its beamsequentially along said axes in said plane; and said synchronizing meansincluding means for relating the object path position data relative tosaid axes representing the same various object positions along thecircular path, and said comparison and outputting means being adapted tocompare the corresponding actual and desired path position data at eachof said object path positions and to output signals representing theactual and desired object path positions to a printer or plotter toprovide a first circle-like display representing the actual objectmovement along said circular path and a second circular displayoverlying said first display so that the object position error at thevarious path positions is visually seen.
 7. The system of claim 6wherein said synchronizing means includes means permitting thesequentially obtained object position data along each of said axes to betaken at random starting times by identifying the maximum, minimum andmean (i.e. half way between the minimum and maximum) actual and desiredobject position data values and rearranging the stored data so that themaximum, mean and minimum object position values of the data for oneaxis is related to the mean, minimum and maximum values of the datataken for the other axis.
 8. The system of claim 6 wherein said signalprocessing means includes means for multiplying the object positionerror data and re-combining the multiplied data with the actual positiondata so that when outputted to said printer or plotter the firstcircle-like display representing the actual object path can be readilyseen although adjacent to said second circular display representing thedesired object path.
 9. The system of claim 1 combined with said object,and said at least one reflecting means is mounted on said object andsaid at least one beam directing means is mounted on a stationarysurface.
 10. The system of claim 1 wherein there is associated with eachof the one or more beam directing means only one reflecting means whichis a flat mirror, and the one or more beam directing means is adapted todirect a diverging beam at right angles to the associated flat mirror.11. The system of claim 10 combined with said object, and said flatmirror associated with each of said one or more beam directing meansbeing mounted on said object.
 12. The system of claim 1 combined withsaid object and wherein there is provided a different beam directingmeans for each of said axes and oriented to direct its beam parallel tothe associated axis, and there being a different one of said at leastone reflecting means associated beam reflecting means mounted tointercept the beam directed from the associated beam directing means,and there is provided means for simultaneously operating said beamdirecting means to simultaneously collect and process the actual objectposition data.
 13. The system of claim 1 wherein each of said one ormore beam directing and associated beam reflecting means form an objectposition measuring system like that shown in FIG.
 1. 14. The system ofclaim 1 wherein each of said one or more beam directing and associatedbeam reflecting means forms an object position measuring means like thatshown in FIG.
 2. 15. The system of claim 1 where each of said one ormore beam directing and associated beam reflecting means forms an objectposition measuring means like that shown in FIG. 3A.
 16. The system ofclaim 1 wherein the object is to be moved along said path where at someof the path positions thereof the object is to desirably to be rotatedor pivoted producing a desired angular motion; and there is providedadded beam directing, reflector and processing means for measuring theactual angular motion of the object at each of said path positions, andcomparing the actual with the desired angular motions of the objectthereat to provide a measure of the angular movement accuracy of theobject moving apparatus.
 17. A method for determining the degree ofaccuracy with which an object is moved along a given path in a spacehaving at least two orthogonal axes by object moving apparatus having adifferent motor for imparting object movement relative to saidrespective axes, said apparatus having programming means having storedin the memory thereof desired object path position data relative to saidaxes for various reference sampling times, and means responsive to saiddesired path position data for generating motor-energizing signals forsaid respective motors to desirably move said object along said desiredpath; said method comprising the steps of: providing one or more beamdirecting means for directing beams of energy respectively to bedirected parallel to each of said orthogonal axes and one or more beamreflecting means associated with each of said one or more beam directingmeans for reflecting each of said beams of energy along one or more beampaths which will ultimately return each beam back to its associated beamdirecting means, at least one of the reflecting means associated witheach beam directing means which first receives the directed beam beingsufficiently large that it receives said beam even when said object ismoved in directions along a circular or other path shape which deviatesfrom the directions said beams are directed, mounting one of each ofsaid beam directing means and said at least one reflecting meansassociated therewith which first receives the beam from its associatedbeam directing means on said object and the other on a stationarysurface; providing signal processing means including means responsive tothe return of each reflected beam of energy to the associated beamdirecting means for developing actual object path position dataindicating the actual displacement of said object relative to said axesat sampling times coincident with said reference times; and datacollection, storage, and comparing means for collecting and storing saiddesired and actual object path position data relative to said axes atsaid sampling times, and for comparing the stored desired and actualpath position data at said sampling times and indicating the degree ofpath position error relative to said axes at said sampling times; anddirecting said one or more beams parallel to said axes and operatingsaid object moving apparatus to move said body along a supposed desiredpath while said data processing means develops, collects and stores saidactual object path position data, compares the stored desired and actualpath position data and indicates the degree of position error resultingfrom said comparison operation.
 18. The method of claim 17 where thereis provided a separate beam directing means for each of said axes andsaid separate beam directing means are simultaneously directedrespectively along said axes simultaneously to collect said object pathposition data.
 19. The method of claim 17 wherein there is provided onlyone of said beam directing means which is sequentially directed alongsaid axes as said object is moved along the supposed desired path assaid processing means then sequentially carries out said functionsthereof.
 20. The method of claim 19 wherein said processing meansincludes synchronizing means of said processing means for relating theactual sequentially obtained object position data relative to saidrespective axes taken in time sequence to the same positions of saidobject along its path of movement following which said processing meanscarries out said comparison function.
 21. The method of claim 20 used tocollect and process object position data where the object is moved in acircular path in a given plane having two orthognal axes and whereinsaid processing means calculates from the data stored for each sampledposition of said object the deviation of the object movement from aperfect circle.
 22. The method of claim 21 wherein said processing meansfirst multiplies the position error data, combines the multiplies errordata with said desired object position data relative to said two axesand effects the display of a first given imperfect circular-like curverepresenting the modified actual circular path of said object in saidplane, and combines said desired object position data relative to saidaxes and effects the display over said first given imperfect circularcurve the circular curve produced by said actual object position datarelative to said axes.
 23. The method of claim 17 wherein said beamdirecting and associated reflecting means form an object positionmeasuring means like that shown in FIG.
 1. 24. The method of claim 17wherein said beam directing and associated reflecting means form anobject position measuring system like that shown in FIG.
 2. 25. Themethod of claim 17 wherein said beam directing and associated reflectingmeans forms an object position measuring system like that shown in FIG.3.
 26. The method of claim 17 wherein said beam directing and associatedreflecting means forms an object position measuring system like thatshown in FIG. 3A.
 27. The method of claim 21 wherein said comparisonmeans first computes the path position error relative to said axes andthen combines the axis position error to provide an indication of polarposition error.
 28. A method for determining the degree of accuracy withwhich an object is desirably moved along or with respect to variousreference points along a given path in a space having at least twoorthogonal axes by object moving apparatus; said method comprising thesteps of: providing one or more beam directing means for directing beamsof energy respectively to be directed parallel to each of saidorthogonal axes and one or more beam reflecting means associated witheach of said one or more beam directing means for reflecting each ofsaid beams of energy along one or more beam paths which will ultimatelyreturn each beam back to its associated beam directing means, at leastone of the reflecting means associated with each beam directing meanswhich first receives the directed beam being sufficiently large that itreceives said beam even when said object is moved in directions along acircular or other path shape which deviates from the directions saidbeams are directed, mounting one of each of said beam directing meansand said at least one reflecting means associated therewith which firstreceives the beam from its associated beam directing means on saidobject and the other on a stationary surface; providing signalprocessing means including means responsive to the return of eachreflected beam of energy to the associated beam directing means formeasuring and storing the degree of actual object movement relative tosaid axes at said path reference points as the object is moved to saidpath reference points; and data collection, storage, and comparing meansfor collecting and storing the desired and said measured actual objectmovement at said path reference points, and for comparing the storeddesired and actual object movement data for said reference points andindicating the degree of deviation of said actual from the desiredobject movement; and directing said one or more beams parallel to saidaxes and operating said object moving apparatus to impart the desiredmovement of said body at said path reference points while said beamdirecting means directs said beams along said axes and said dataprocessing means develops, collects and stores said actual objectmovement data, compares the stored desired and actual measured objectmovement at said path reference points and indicates the degree ofmovement error resulting from said comparison operation.